The announcement, made on Tuesday, followed criticism from Darwin's Mayor asking why federal politicians had not shown more interest in the 120,000 people in the Top End affected by Tropical Cyclone Marcus.

Kon Vatskalis said he was disappointed and the Northern Territory should "absolutely" ask for federal assistance, which as of Tuesday morning had not been offered to help with the disaster recovery effort.

"I know very well there are fires down south, I know politicians and the Prime Minister have visited those areas, and well done for that," Mr Vatskalis told ABC Radio Darwin on Tuesday.

"But I think somebody should show some interest for the 120,000 people here in Darwin who went through that.

"They had their lives interrupted, their power interrupted, they had their roads closed down, but I'm very, very disappointed not to see response from our political leaders down in Canberra."

Council to look at removing dangerous mahogany trees

Mr Vatskalis said he would bring a motion before council to look at removing African mahoganies that pose a risk to life or property.

Two people are known to have been killed by falling branches from the trees in the Top End, including golfer William Brown in 2014.

The NT Coroner found his death was preventable, and the council and golf course had been negligent in their maintenance of the trees.

He recommended six-monthly inspections.

Mr Vatskalis said there had been an inspection of the council's mahoganies "a few months ago".

He said he wanted to see the planting of more trees suitable to the Top End's tropical climate.

"Mahoganies where they grow in Africa have a very big tap root that goes down deep looking for water," he said.

"Here, we plant them in parks where they are watered nearly every day so they don't have to go down, they just spread out to absorb as much water as possible.

"And of course by spreading their roots out with a huge canopy, like the one they've got, they actually topple over very quickly if there is a strong blow and if the soil is wet."

Anyone affected by fallen council trees should contact the council immediately, Mr Vatskalis said.

Power still down to some homes, traffic lights

Meanwhile, all but 20 schools in the Darwin region reopened on Tuesday morning, along with Charles Darwin University, and public servants have been urged to go back to work.

However, some traffic lights were still not functioning and many roads remain littered with trees and debris so motorists are warned to take care on the roads.

Power has been restored to several thousand more homes.

Of the almost 30,000 homes that lost power on Saturday, 6,000 remain unconnected at Dundee, Lambells Lagoon, and Middle Point, but Power and Water expected to have them all reconnected by Wednesday, with repair works underway around the clock since the storm.

Around 300 Defence Force personnel, joined by 50 US marines, descended on the region to assist with the clean-up.

Major George Forbes, from the United States Marine Corp, said it was the first time troops had been asked to respond to a cyclone, and he hoped it would be the last "for everyone's sake".

"The community has been a gracious host to us while we've been here, and what little bit we can do is a tangible demonstration to the US and Australian alliance," he said.

"I couldn't believe how many trees came down ... it did a considerable amount of damage."

The clean-up of the city will take at least another week, before council continues cleaning up green waste left on verges.

Tropical cyclone watch alert could be issued on Wednesday

The weather bureau is monitoring a weak tropical low that has formed off northern Australia, which could develop into another cyclone before the weekend.

With the threat of Tropical Cyclone Marcus now past and Darwin residents still cleaning up, focus has turned to the weak tropical low that is shaping up in the Torres Strait.

It could intensify in the next 36 hours and is expected to move west into the Arafura Sea towards east Arnhem Land in the Northern Territory over the coming days, the Northern Territory Bureau of Meteorology said.

The community of Nhulunbuy, on the Gove Peninsula, could be affected.

"Conditions are pretty favourable for development, so we expect it to turn into a tropical cyclone on Thursday or Friday," duty forecaster Peter Markworth said.

"We'll keep reassessing, but at this stage we could be issuing a watch [alert] as early as Wednesday.

"At this stage, it's very unlikely that Darwin will be affected by it."

The next cyclone to form in Australian waters will be named Nora.

ABC

Data Sources

Weather information based on data supplied by the Bureau of Meteorology and other sources